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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Gas, Stars, and Star Formation in Alfalfa Dwarf Galaxies

We examine the global properties of the stellar and Hi components of 229 low H i mass dwarf galaxies extracted from the ALFALFA survey, including a complete sample of 176 galaxies with H i masses <10(sup 7.7) solar mass and Hi line widths <80 kilometers per second. Sloan Digital Sky Survey (SDSS) data are combined with photometric properties derived from Galaxy Evolution Explorer to derive stellar masses (M*) and star formation rates (SFRs) by fitting their UV-optical spectral energy distributions (SEDs). In optical images, many of the ALFALFA dwarfs are faint and of low surface brightness; only 56% of those within the SDSS footprint have a counterpart in the SDSS spectroscopic survey. A large fraction of the dwarfs have high specific star formation rates (SSFRs), and estimates of their SFRs and M* obtained by SED fitting are systematically smaller than ones derived via standard formulae assuming a constant SFR. The increased dispersion of the SSFR distribution at M* approximately less than10(exp 8)M(sub 0) is driven by a set of dwarf galaxies that have low gas fractions and SSFRs; some of these are dE/dSphs in the Virgo Cluster. The imposition of an upper Hi mass limit yields the selection of a sample with lower gas fractions for their M* than found for the overall ALFALFA population. Many of the ALFALFA dwarfs, particularly the Virgo members, have H i depletion timescales shorter than a Hubble time. An examination of the dwarf galaxies within the full ALFALFA population in the context of global star formation (SF) laws is consistent with the general assumptions that gas-rich galaxies have lower SF efficiencies than do optically selected populations and that Hi disks are more extended than stellar ones.

ALFALFA↗
NASA NTRS2014

Timing of Formation of a Wassonite-bearing Chondrule

Wassonite, ideally stoichiometric TiS, is a titanium monosulfide recently discovered in the Yamato 691 EH3 enstatite chondrite. Wassonite grains were located within the mesostasis of a single barred olivine chondrule. Such chondrules likely formed in the solar nebula by melting of fine grained precursor dust. The reduced nature of enstatite chondrites, and the wassonite-bearing chondrule in particular, may suggest precursor materials included Ti-bearing troilite, metallic Fe-Ni, and possibly graphite. Under the reducing conditions present in enstatite chondrites S can partition more readily into silicate melt, leading to raised Ti content of the residual Fe-FeS melt. By the time sulfide crystallized from the melt, the Ti concentration was high enough to form small grains of pure TiS - wassonite. As a mineral not previously observed in nature wassonite and its host chondrule may provide additional constraints on physical and chemical conditions in the solar nebula at a specific time and location relevant to planetary formation. Enstatite chondrites and Earth share similar isotopic compositions of Cr, Ni, Ti, O and N. Understanding the formation conditions of enstatite chondrite chondrules may therefore have wider relevance for terrestrial planet accretion and other early inner solar system processes. Here we present preliminary results of an investigation of the Al-Mg systematics of the only known wassonite-bearing chondrule. The goal of this study is to determine whether this chondrule's formation was contemporaneous with other enstatite chondrite chondrules and to establish its place in the broader timeline of solar system events.

Needham, A. W.↗
NASA NTRS2014

Consensus-Based Formation Control of a Class of Multi-Agent Systems

This paper presents a consensus-based formation control scheme for autonomous multi-agent systems represented by double integrator dynamics. Assuming that the information graph topology consists of an undirected connected graph, a leader-based consensus-type control law is presented and shown to provide asymptotic formation stability when subjected to piecewise constant formation velocity commands. It is also shown that global asymptotic stability is preserved in the presence of (0, infinity)- sector monotonic non-decreasing actuator nonlinearities.

Joshi, Suresh↗
NASA NTRS2014

Directly Imaging Damped Ly-Alpha Galaxies at Redshifts Greater Than 2. III: The Star Formation Rates of Neutral Gas Reservoirs at Redshifts of Approximately 2.7

We present results from a survey designed to probe the star formation properties of 32 damped Ly alpha systems (DLAs) at redshifts of approximately 2.7. By using the "double-DLA" technique that eliminates the glare of the bright background quasars, we directly measure the rest-frame FUV flux from DLAs and their neighbouring galaxies. At the position of the absorbing gas, we place stringent constraints on the unobscured star formation rates (SFRs) of DLAs to 2 sigma limits of psi less than 0.09−0.27 solar mass yr(exp −1), corresponding to SFR surface densities sigma(sub sfr) less than 10(exp −2.6)−10(exp −1.5) solar mass yr(exp −1) kpc(exp −2). The implications of these limits for the star formation law, metal enrichment, and cooling rates of DLAs are examined. By studying the distribution of impact parameters as a function of SFRs for all the galaxies detected around these DLAs, we place new direct constraints on the bright end of the UV luminosity function of DLA hosts. We find that less than or equal to 13% of the hosts have psi greater than or equal to 2 solar mass yr(exp −1) at impact parameters b(sub dla) less than or equal to (psi/solar mass yr(exp −1))(exp 0.8) + 6 kpc, differently from current samples of confirmed DLA galaxies. Our observations also disfavor a scenario in which the majority of DLAs arise from bright LBGs at distances 20 less than or equal to b(sub dla) less than 100 kpc. These new findings corroborate a picture in which DLAs do not originate from highly star forming systems that are coincident with the absorbers, and instead suggest that DLAs are associated with faint, possibly isolated, star-forming galaxies. Potential shortcomings of this scenario and future strategies for further investigation are discussed.

Directly↗
NASA NTRS2015

Impact-Induced Clay Mineral Formation and Distribution on Mars

Clay minerals have been identified in the central peaks and ejecta blankets of impact craters on Mars. Several studies have suggested these clay minerals formed as a result of impact induced hydrothermalism either during Mars' Noachian era or more recently by the melting of subsurface ice. Examples of post-impact clay formation is found in several locations on Earth such as the Mjolnir and Woodleigh Impact Structures. Additionally, a recent study has suggested the clay minerals observed on Ceres are the result of impact-induced hydrothermal processes. Such processes may have occurred on Mars, possibly during the Noachian. Distinguishing between clay minerals formed preor post-impact can be accomplished by studying their IR spectra. In fact, showed that the IR spectra of clay minerals is greatly affected at longer wavelengths (i.e. mid-IR, 5-25 micron) by impact-induced shock deformation while the near-IR spectra (1.0-2.5 micron) remains relatively unchanged. This explains the discrepancy between NIR and MIR observations of clay minerals in martian impact craters noted. Thus, it allows us to determine whether a clay mineral formed from impact-induced hydrothermalism or were pre-existing and were altered by the impact. Here we study the role of impacts on the formation and distribution of clay minerals on Mars via a fully 3-D Monte Carlo cratering model, including impact- melt production using results from modern hydrocode simulations. We identify regions that are conducive to clay formation and the location of clay minerals post-bombardment.

Rivera-Valentin, E. G.↗
NASA NTRS2016

Synthesis of Akaganeite in the Presence of Sulfate: Implications for Akaganeite Formation in Yellowknife Bay, Gale Crater, Mars

Akaganeite (beta-FeOOH) is an Fe(III) (hydr)oxide with a tunnel structure usually occupied by chloride. Akaganeite has been recently discovered in a mudstone on the surface of Mars by the Chemistry and Mineralogy (CheMin) and Sample Analysis at Mars (SAM) instruments onboard the Mars Science Laboratory (MSL) Curiosity Rover in Gale crater [1, 2]. Akaganeite was detected together with sulfate minerals [anhydrite (CaSO4) and basanite (2CaSO4·2H2O)] in the drilled Cumberland and John Clein mudstone samples at Yellowknife Bay [2]. Discovery of akaganeite and sulfates in the same samples suggests that sulfate ions could be present in aqueous solution during akaganeite formation. However, mechanism and aqueous environmental conditions of akaganeite formation (e.g., pH and range of sulfate concentration) in Yellowknife Bay remain unknown. The objective of our work was to perform synthesis of akaganeite without or with sulfate addition at variable pHs in order to constrain formation conditions of akaganeite in Yellowknife Bay, Gale crater on Mars.

Peretyazhko, T. S.↗
NASA NTRS2016

Authigenesis/Diagenesis of the Murray Formation Mudstone in Gale Crater, Mars

The Mars Science Laboratory rover Curiosity has been exploring sedimentary deposits in Gale crater since August, 2012. The rover has traversed up section through approximately 150 m of sedimentary rocks deposited in fluvial, deltaic, and lacustrine environments (Bradbury group and overlying Mount Sharp group). The Murray formation lies at the base of the Mt. Sharp group and has been interpreted to be a finely laminated mudstone likely deposited in a subaqueous lacustrine environment. Four drill samples from several elevations in the Murray fm have been acquired by the rover's sampling system and delivered to the CheMin XRD instrument. The lower section of the Murray fm contains 2:1 phyllosilicate(s), hematite, jarosite, XRD amorphous materials, and primary basaltic minerals. Further up section, the Murray fm contains magnetite, cristobalite, tridymite, abundant Si-rich XRD amorphous materials along with plagioclase and K-feldspars. Murray formation materials appear to have been altered under an open hydrologic system based on the bulk chemistry of these materials measured by the Alpha Particle X-ray Spectrometer (APXS). The 2:1 phyllosilicate only occurs in the lowermost section of the Murray fm and may be detrital or formed during authigenesis of Murray fm materials, similar to the Fe-saponite and magnetite detected in a mudstone in the Yellowknife Bay fm near Curiosity's landing site (stratigraphically at the base of the Bradbury group). The occurrence of jarosite and hematite in the lower section indicates an acidic diagenetic event. These phases may have formed via several acidic alteration mechanisms, including (1) oxidative weathering of mafic igneous rocks containing sulfides; (2) sulfuric acid weathering of Fe-bearing phases; and (3) near-neutral pH subsurface solutions rich in Fe2(+) that were rapidly oxidized to Fe3(+), which produced excess acidity. The transition from abundant hematite in the lowermost Murray fm to magnetite moving up section may indicate changes in lake chemistry, i.e., variable redox conditions, possibly during authigenesis or subsequent diagenetic events. Tridymite, a high temperature mineral, (and possibly cristobalite) is detrital, potentially deposited in a lake from a distal silicic volcanic rock source or from crustal materials present prior to the Gale Crater impact event. Abundant Si-rich XRD amorphous materials in the upper sections of the Murray fm may be detrital or an aqueous alteration product of primary igneous phases and phyllosilicates. Curiosity's science team is still deciphering the authigenesis and diagenetic events that formed the Murray fm. The mineralogy and geochemistry of the formation suggest a complicated history with several (many?) episodes of aqueous alteration under a variety of environmental conditions.

Ming, D. W.↗
NASA NTRS2016

Formation of Oxides in the Interior of Friction Stir Welds

In friction stir welding (FSWing) the actual solid state joining takes place between the faying surfaces which form the weld seam. Thus the seam trace is often investigated for clues when the strength of the weld is reduced. Aluminum and its alloys are known to form a native, protective oxide on the surface. If these native surface oxides are not sufficiently broken up during the FSW process, they are reported to remain in the FSW interior and weaken the bond strength. This type of weld defect has been referred to as a lazy "S", lazy "Z", joint line defect, kissing bond, or residual oxide defect. Usually these defects are mitigated by modification of the process parameters, such as increased tool rotation rate, which causes a finer breakup of the native oxide particles. This study proposes that there may be an alternative mechanism for formation of oxides found within the weld nugget. As the oxidation rate increases at elevated temperatures above 400ºC, it may be possible for enhanced oxidation to occur on the interior surfaces during the FSW process from entrained air entering the seam gap. Normally, FSWs of aluminum alloys are made without a purge gas and it is unknown how process parameters and initial fit up could affect a potential air path into the interior during the processing. In addition, variations in FSW parameters, such as the tool rotation, are known to have a strong influence on the FSW temperature which may affect the oxidation rate if internal surfaces are exposed to entrained air. A series of FSWs were made in 3 different thickness panels of AA2219 (0.95, 1.27 and 1.56 cm) at 2 different weld pitches. As the thickness of the panels increased, there was an increased tendency for a gap to form in advance of the weld tool. If sufficient air is able to enter the workpiece gap prior to consolidation, the weld temperature can increase the oxidation rate on the interior surfaces. These oxidation rates would also be accelerated in areas of localized liquation. Metallographs from the weld panels showed indications of liquation at the grain boundaries. In FSWs of thicker panels, these regions of liquation were found to be heavily oxidized. The quality of the FSWs was evaluated from tensile testing at room temperature. As the panel thickness increased, a slight decrease in tensile strength was observed which was attributed to the presence of oxides. No oxide formation was observed in the thinner workpieces, although there were indications of localized liquation at the grain boundaries. Results from this study will assist in a better understand of the mechanisms of oxide formation in FSW interiors and provide methodology for minimizing their occurrence.

Schneider, Judy↗
NASA NTRS2016

Initial Satellite Formation Flight Results from the Magnetospheric Multiscale Mission

This paper describes the underlying dynamics of formation flying in a high-eccentricity orbit such as that of the Magnetospheric Multiscale mission. The GPS-based results used for MMS navigation is summarized, as well as the procedures that are used to design the maneuvers used to place the spacecraft into a tetrahedron formation and then maintain it. The details of how to carry out these maneuvers are then discussed. Finally, the numerical results that have been obtained concerning formation flying for the MMS mission to date (e.g. tetrahedron sizes flown, maneuver execution error, fuel usage, etc.) are presented in detail.

Conjunction↗
NASA NTRS2016

Mechanisms for the Formations of the Thymine Under Astrophysical Conditions and Implications for the Origin of Life

Nucleobases are the carriers of the genetic information in ribonucleic acid and deoxyribonucleic acid (DNA) for all life on Earth. Their presence in meteorites clearly indicates that compounds of biological importance can form via non-biological processes in extraterrestrial environments. Recent experimental studies have shown that the pyrimidine-based nucleobases uracil and cytosine can be easily formed from the ultraviolet irradiation of pyrimidine in H2O-rich ice mixtures that simulate astrophysical processes. In contrast, thymine, which is found only in DNA, is more difficult to form under the same experimental conditions, as its formation usually requires a higher photon dose. Earlier quantum chemical studies confirmed that the reaction pathways were favorable provided that several H2O molecules surrounded the reactants. However, the present quantum chemical study shows that the formation of thymine is limited because of the inefficiency of the methylation of pyrimidine and its oxidized derivatives in an H2O ice, as supported by the laboratory studies. Our results constrain the formation of thymine in astrophysical environments and thus the inventory of organic molecules delivered to the early Earth and have implications for the role of thymine and DNA in the origin of life.

Origin↗
NASA NTRS2017

Smectite Formation in Acid Sulfate Environments on Mars

Phyllosilicates of the smectite group detected in Noachian and early Hesperian terrains on Mars were hypothesized to form under aqueous conditions that were globally neutral to alkaline. These pH conditions and the presence of a CO2-rich atmosphere should have been favorable for the formation of large carbonate deposits. However, large-scale carbonate deposits have not been detected on Mars. We hypothesized that smectite deposits are consistent with perhaps widespread acidic aqueous conditions that prevented carbonate precipitation. The objective of our work was to investigate smectite formation under acid sulfate conditions in order to provide insight into the possible geochemical conditions required for smectite formation on Mars. Hydrothermal batch incubation experiments were performed with Mars-analogue, glass-rich, basalt simulant in the presence of sulfuric acid of variable concentration.

Peretyazhko, T. S.↗
NASA NTRS2017

Meteorological Support Interface Control Working Group (MSICWG) Instrumentation, Data Format, and Networks Document

The purpose of this document is to provide an overview of instrumentation discussed at the Meteorological Interface Control Working Group (MSICWG), a reference for data formats currently used by members of the group, a summary of proposed formats for future use by the group, an overview of the data networks of the group's members. This document will be updated as new systems are introduced, old systems are retired, and when the MSICWG community necessitates a change to the formats. The MSICWG consists of personnel from the National Aeronautics and Space Administration (NASA) Kennedy Space Center (KSC), NASA Marshall Space Flight Center (MSFC), NASA Johnson Space Center (JSC), National Oceanic and Atmospheric Administration National Weather Service Spaceflight Meteorology Group (SMG), and the United States Air Force (USAF) 45th Space Wing and Weather Squadron. The purpose of the group is to coordinate the distribution of weather related data to support NASA space launch related activities.

Brenton, James↗
NASA NTRS2017

Chandra Reveals Heavy Obscuration and Circumnuclear Star Formation in Seyfert 2 Galaxy NGC 4968

We present the Chandra imaging and spectral analysis of NGC 4968, a nearby (z = 0.00986) Seyfert 2 galaxy. We discover extended (approx. 1 kpc) X-ray emission in the soft band (0.5-2 keV) that is neither coincident with the narrow line region nor the extended radio emission. Based on spectral modeling, it is linked to on-going star formation [approx. 2.6-4 Mass compared to Earth yr(exp.− 1)]. The soft emission at circumnuclear scales (inner approx. 400 pc) originates from hot gas, with kT approx. 0.7 keV, while the most extended thermal emission is cooler (kT approx. 0.3 keV). We refine previous measurements of the extreme Fe K alpha equivalent width in this source (EW 2.5 + 2.6/-1.0 keV), which suggests the central engine is completely embedded within Compton-thick levels of obscuration. Using physically motivated models fit to the Chandra spectrum, we derive a Compton-thick column density [N(sub H) is greater than 1.25× 10(exp 24) cm(exp.− 2)] and an intrinsic hard (2-10 keV) X-ray luminosity of approx. 3-8× 10(exp. 42) erg s(exp. − 1) (depending on the presumed geometry of the obscurer), which is over two orders of magnitude larger than that observed. The large Fe K Alpha EW suggests a spherical covering geometry, which could be confirmed with X-ray measurements above 10 keV. NGC 4968 is similar to other active galaxies that exhibit extreme Fe K Alpha EWs (i.e., greater than 2 keV) in that they also contain on-going star formation. This work supports the idea that gas associated with nuclear star formation may increase the covering factor of the enshrouding gas and play a role in obscuring active galactic nuclei.

LaMassa, Stephanie M.↗
NASA NTRS2017

Major Pathways to Electron Distribution Function Formation in Regions of Diffuse Aurora

This paper discusses the major pathways of electron distribution function formation in the region of diffuse aurora. The diffuse aurora accounts for about of 75% of the auroral energy precipitating into the upper atmosphere, and its origin has been the subject of much discussion. We show that an earthward stream of precipitating electrons initially injected from the Earth's plasma sheet via wave-particle interactions degrades in the atmosphere toward lower energies and produces secondary electrons via impact ionization of the neutral atmosphere. These electrons of magnetospheric origin are then reflected back into the magnetosphere along closed dipolar magnetic field lines, leading to a series of reflections and consequent magnetospheric interactions that greatly augment the initially precipitating flux at the upper ionospheric boundary (700-800 km). To date this, systematic magnetosphere-ionosphere coupling element has not been included in auroral research models, and, as we demonstrate in this article, has a dramatic effect (200-300%) on the formation of the precipitating fluxes that result in the diffuse aurora. It is shown that wave-particle interaction processes that drive precipitating fluxes in the region of diffuse aurora from the magnetospheric altitudes are only the first step in the formation of electron precipitation at ionospheric altitudes, and they cannot be separated from the atmospheric collisional machine that redistributes and transfers their energy inside the magnetosphere-ionosphere-atmosphere coupling system.

magnetospheric↗
NASA NTRS2018

Formation Flight System Extremum-Seeking-Control Using Blended Performance Parameters

An extremum-seeking control system for formation flight that uses blended performance parameters in a conglomerate performance function that better approximates drag reduction than performance functions formed from individual measurements. Generally, a variety of different measurements are taken and fed to a control system, the measurements are weighted, and are then subjected to a peak-seeking control algorithm. As measurements are continually taken, the aircraft will be guided to a relative position which optimizes the drag reduction of the formation. Two embodiments are discussed. Two approaches are shown for determining relative weightings: "a priori" by which they are qualitatively determined (by minimizing the error between the conglomerate function and the drag reduction function), and by periodically updating the weightings as the formation evolves.

Ryan, John J.↗
NASA NTRS2018

A Prognostics Framework Development for Swarm Satellite Formations

Prognostics is the science of predicting the failure(s) of a component or a system and understanding how the performance will change in the event of a failure or degradation mechanism. With accurate predictions of possible failures, autonomous mitigative actions can be taken to correct/repair any issues or alert human operators of a failure threshold exceedance requiring condition-based maintenance. Although there is extensive research on failure predictions for a component or a system, there are significantly more opportunities to foray into failure predictions and prognostics for a system of systems such as an airspace consisting of multiple aircraft, a fleet of unmanned aerial vehicles, and a swarm of intelligent satellite systems. Failure prediction and mitigation are particularly important in autonomous systems such as satellite swarm systems that need effective resource management and minimal human interactions. Based on NASA's decadal survey, there is a clear need to prioritize the development of satellite swarm technology for studies of space physics and Earth science. The science community will propose future missions that return in-situ measurements from a 3-D (three-dimensional) volume of space, with relative spacecraft motion and inter-satellite baselines controlled according to the mission objectives. For such multi-spacecraft missions, it is required that ground operations resources do not scale with the number of satellites, thus compromising the swarm or leading to inefficiencies in resource allocation. Swarms of tens or hundreds of small satellites will require autonomy in attitude control, navigation and failure. Although significant research has been conducted in the areas of autonomous formation flying algorithms, less attention has been given to the development of resilient systems robust to failures.The focus of this research paper is the integration of model-based prognostics into the swarm dynamics control and decision-making algorithms. We simulate swarm management strategies for a subsystem failure to demonstrate the importance of failure predictions by comparing two cases: (i) no health information is provided to the system and utilized in the decision-making process and (2) system health information is obtained using prognostics and employed by the control system. One example scenario presented is for the GPS (Global Positioning System) system of an individual satellite to perform off-nominally due to increasing estimated error. In this scenario, the keep-out zone for that satellite would become more conservative, thereby decreasing the risk of collision. This is achieved via tuning the individual artificial repulsive functions assigned to each satellite.This paper is structured as follows. First we provide an overview of current swarm technology development, where we specifically use the term swarm to define multiple satellites flying in formation in similar orbits, with cross-link communication and station-keeping capabilities. Second, we give an introduction to the Swarm Orbital Dynamics Advisor (SODA), a tool that accepts high-level configuration commands and provides the orbital maneuvers required to achieve the prescribed formation configuration. Third, we provide the details of the model-based prognostics algorithm implementation in SODA. Finally, we present different case studies for potential component/subsystem failures and the swarm responses based with and without failure prediction information.

prognostics↗
NASA NTRS2018

Considerations When Building Thermal Models that Require Conversion Between Formats

At times, it is inevitable to require conversion of thermal models from one software format to another. This most often occurs for missions with international partners where not all parties utilize the same software packages for thermal analysis. Mandating a single tool for all parties is one possible solution, but this approach can introduce problems if significant effort is required to overcome inexperience with the designated tool and may result in difficulty meeting analysis schedule requirements. Alternatively, allowing all parties to use their own familiar tools minimizes the impact to analysis schedules but does introduce the need to convert the models later to a common format for analysis at a higher level of assembly. External conversion tools and formats have been developed through the years to aid in this process, but have had limited success in fully converting models seamlessly. Having a basic familiarity with tool capabilities on both sides of the conversion process allows for models to be built in a manner to better facilitate conversion by avoiding features and capabilities which are unsupported by the destination tool or for which no workarounds exist. Also, the effort to convert a model is often neglected when developing the schedules for analysis at the higher assembly levels; delivery of models preconditioned for convertibility minimizes the schedule risk. This paper seeks to provide some guidance on modeling techniques to avoid when developing Geometrical Math Models (GMM) and Thermal Math Models (TMM) when conversion is required. The recommendations are based on GMM conversion experiences between TSS/ThermalDesktop/ESARAD and TMM conversions between SINDA-FLUINT/ESATAN.

Modeling↗
NASA NTRS2018

Experimentation to Understand Planet and Proto-Planet Formation

Experimental petrology has placed constraints on a wide variety of nebular and planet formation processes such as chondrule formation, CAI (Calcium-Aluminum-rich Inclusions) crystallization, asteroid magmatism, mantle melting, core formation, element partitioning related to radiogenic isotopes and heat production. Although great progress has been made, there remain several key problems where more data are required to constrain modelling, both empirical and thermodynamics-based. Here I will focus on several areas with implications for meteoritics and planetary science, including systems of low fO2 (Oxygen fugacity), constructing models that include both metal and silicate for mantle melting and differentiation, high pressure phase equilibria relevant to full range of silicate mantles, and core-mantle equilibria where H and O are specified, and their effects are measured.

Righter, K.↗